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• A novel 3D anisotropic random porous structure based on anisotropic Voronoi diagrams with high strength and high stiffness. • The parallel 3D anisotropic Voronoi diagram algorithm which eliminates the need for iterative calculations and is applicable to complex 3D shapes, including intricate concave shapes and structures with non-zero genus. • The stress driven strategy in which the distribution of Voronoi cells is related with the spatial distribution of stress magnitudes, while the cell orientations are controlled by the direction of stress tensor. Porous structures exhibit excellent mechanical properties and are widely utilized in engineering design. However, there is still substantial potential for enhancing the mechanical performance of these structure. By customizing the anisotropic design of each pore in the porous structure, the strength and stiffness of the structure can be significantly enhanced. In this work, we present a novel method for designing 3D anisotropic Voronoi porous structures (AVPSs). To construct these structures, we propose a novel algorithm for generating 3D anisotropic Voronoi diagrams (AVDs) based on Riemannian distance. The geometries of Voronoi cells are controlled to conform with both the stress distribution and the principal stress directions. The distribution of Voronoi cells are graded using a stress-based site sampling strategy, the orientation of Voronoi cells are modified by introducing stress-mapped Riemann tensor fields. The AVPSs are then modeled by computing implicit surfaces based on AVDs. The AVPSs conform closely to the geometric profile of the input model by clipping AVDs using the tetrahedral mesh. Furthermore, the results obtained from numerical simulations and experimental tests indicate that the AVPSs possess both high strength and high stiffness. [ABSTRACT FROM AUTHOR]

This paper extends the high-order entropy stable (ES) adaptive moving mesh finite difference schemes developed in Duan and Tang (2022) to the two- and three-dimensional (multi-component) compressible Euler equations with the stiffened equation of state (EOS). The two-point entropy conservative (EC) flux is first constructed in the curvilinear coordinates, which is nontrivial in the case of the stiffened EOS. With the aid of the high-order discretization of the geometric conservation laws and the linear combinations of the two-point EC fluxes, the high-order semi-discrete EC schemes are derived. The high-order semi-discrete ES schemes are constructed by adding suitable high-order dissipation term to the EC schemes such that the semi-discrete entropy inequality is satisfied and unphysical oscillations are suppressed. The high-order dissipation term is built on the multi-resolution weighted essentially non-oscillatory (WENO) reconstruction and the newly derived scaled eigenvector matrices. The explicit strong-stability-preserving Runge–Kutta methods are used for the time discretization and the mesh points are adaptively redistributed by iteratively solving the mesh redistribution equations with an appropriate monitor function, which is adapted to the multi-component flow and encodes more physical characteristics of the solutions. Several 2D and 3D numerical tests are conducted on the parallel computer system with the MPI programming to validate the accuracy and the ability to effectively capture the localized structures of the proposed schemes. [ABSTRACT FROM AUTHOR]